Issue 75

P. Grubits et alii, Fracture and Structural Integrity, 75 (2026) 124-156; DOI: 10.3221/IGF-ESIS.75.10

C ONCLUSION

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n this paper, a developed framework is presented for the elastic and elasto-plastic design of truss structures, employing the complementary strain energy of residual forces as a key parameter to quantify inelastic deformations. The proposed methodology is specifically devised to automatically minimize the cross-sectional areas of bar members while ensuring that all structural criteria are satisfied for a safe and feasible solution. This is achieved through the implementation of a relatively complex fitness function, which—in addition to structural weight—includes penalty terms for plastic deformations, load-bearing capacity, and global stability. A displacement constraint is also integrated to account for serviceability requirements. Furthermore, the framework is capable of incorporating plastic material behavior, large deformation effects, and initial geometric imperfections, thereby enabling highly accurate and realistic structural designs. The entire approach is implemented using the ABAQUS finite element software in conjunction with the PYTHON programming language. To demonstrate the efficiency, flexibility, and potential of the proposed design strategy, two well-known benchmark structures—the 37-bar and 25-bar trusses—are investigated. For the former, three distinct optimization setups are examined: E1-OP1, based on purely elastic design criteria; E1-OP2, incorporating elasto-plastic analysis by allowing limited inelastic deformations up to a predefined threshold; and E1-OP3, which extends E1-OP2 by introducing a displacement constraint. In the case of the 25-bar truss, two elasto-plastic design scenarios are evaluated: without (E2-OP1) and with (E2 OP2) displacement constraint. Each setup is executed through multiple independent optimization runs to account for the stochastic nature of the genetic algorithm and to ensure a reliable assessment of performance. The key findings are summarized below: 1. In all optimization setups, substantial material savings were achieved while fully satisfying the structural criteria defined for each design scenario. For the 37-bar truss, E1-OP1 led to a weight reduction of approximately 48.5%, E1-OP2 reached 55.7% , and E1-OP3 resulted in 43.7% savings relative to the initial configuration, confirming the framework’s efficiency across varying design objectives. Similarly, for the 25-bar truss, the elasto-plastic optimization without a displacement constraint (E2-OP1) achieved a weight reduction of 19.1%, while the setup incorporating the serviceability criterion (E2-OP2) attained 18.7% savings compared to the reference configuration. In both benchmarks, all structural performance requirements—including load-bearing capacity, stability, and plastic deformation limits—were satisfied, further confirming the robustness and versatility of the proposed optimization framework across different structural configurations. 2. The elasto-plastic design approach without displacement constraint, applied in E1-OP2, results in greater material efficiency compared to the fully elastic scenario in E1-OP1, while still maintaining tight control over inelastic deformations. Within the defined design domain of the 37-bar truss, this strategy achieves an average weight reduction of 16.5%, with plastic deformation remaining negligible. Allowing limited plasticity also enhances convergence, as it permits the identification of lighter configurations capable of tolerating moderate inelastic effects without compromising structural safety. 3. The integration of a displacement constraint further enhances the framework’s versatility by ensuring that the prescribed serviceability limit is only marginally exceeded, while still achieving weight minimization and fulfilling all structural performance requirements, as demonstrated in the E1-OP3 results. This constraint leads to inherently stiffer configurations and results in an average weight increase of approximately 24.0% compared to the best-performing E1 OP2 solutions, which operate without displacement limitations. In the case of the 25-bar truss, both optimization setups—E2-OP1 and E2-OP2—satisfied the prescribed displacement limit, even though it was not explicitly active in the former. This favorable outcome demonstrates that the defined design space inherently promotes sufficiently stiff structural configurations, ensuring compliance with serviceability requirements without additional constraints. Consequently, the displacement limitation exerted minimal influence on the optimization process. Nevertheless, the framework retains the flexibility to impose stricter serviceability limits by adjusting the displacement threshold when necessary, further highlighting the overall robustness, adaptability, and effectiveness of the proposed optimization methodology. In conclusion, the proposed framework facilitates an advanced, automated design process capable of generating material efficient and structurally robust truss configurations. These results underscore the potential of advanced optimization tools to enhance structural engineering practice through more intelligent, performance-driven design methodologies.

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